A fan who threw a banana in the direction of Indigenous Adelaide Crows star Eddie Betts will have her club membership cancelled by Port Adelaide.

Key points:

Fans capture video of woman throwing banana at Betts

Port bans fan, Crows "disgusted and disappointed"

SA Premier says act was "nasty form of racial comment"

Port's chairman David Koch said the club knew who she was but had not yet spoken with her.

"We've revoked the membership not only for this year but also for next year as well," he said.

"Whether we take any further action will be decided on the outcome of the motivation and further investigation.

"If it was racially motivated not only would she be banned for life from the club, we would encourage her to come and sit with our players, our Aboriginal players, and try and understand what these actions mean to them."

The goalsneak then looked into the crowd, dominated by Power fans, before walking away as his team-mates arrived to celebrate with him.

A video appeared on social media shortly after the game showing the woman throwing something at the Indigenous star, which team-mate Josh Jenkins batted away.

Spectator Jamie Christodoulou said he saw the woman throw a banana after Betts had scored.

"A lot of supporters in the area were very disappointed and angered with what she had done," he said.

"We all outed her, I particularly did.

"I pretty much ... told her she was out of line, just took it too far, there's no place for that."

Mr Christodoulou said he and his family, including children, had been forced to put up with the woman's foul language at home games all year.

"This happened in the row in front of me. I am proud to say that I yelled at her and told her she took it too far. She responded by saying, 'but he's just a monkey'."

He said the woman then got up and left.

"Betts did heckle the crowd after he got that goal, but he didn't deserve such a racist act," he said.

The Crows released a statement saying the club was "disappointed and disgusted" by the behaviour of some fans at the Showdown.

"The club has contacted the Port Adelaide Football Club, Adelaide Oval Stadium Management Authority and AFL, and has expressed in the strongest possible terms that we expect significant action to be taken against any person found guilty of anti-social behaviour," it said.

'Nasty form of racial comment': Premier

South Australian Premier Jay Weatherill said he and most other football fans at the game were impressed with Betts's performance.

"As for the idiot who thought throwing a banana was funny, it wasn't. It appears this was just a particularly nasty form of racist comment," he said.

"I am pleased the club has taken strong and immediate action."

Port Adelaide was swift to issue a statement after the video of the incident surfaced, saying it would conduct an investigation.

"Port Adelaide is appalled by the vision and will not tolerate this type of anti-social behaviour at its games," it read.

"Any object thrown onto the field in the direction of players, coaches or umpires is completely unacceptable.

"Port Adelaide implemented a spectator code of conduct in 2014 for all its members and supporters to ensure Adelaide Oval is a family friendly environment at its games."

The AFL is not unfamiliar with controversies pertaining to vilification by its fans.